Proper Time, and FresneVs Coefficient. 655> 



With these values, equation (5) gives 



v'T Am' .„ , 9 dm' IdE E dz d /E\ , n , 



—~*iit =vil ~&w = iw-*rt = dtVzh (7) 



From two factorings of (Qi), an important duplicate 

 expression of T x follows : 



m d , -. dv, ,dv dm' /0 . 



T^-( mi zv) = mi ^= m ' Jt+ v^. . . (8) 



Since an activity of importance for the electron grows out 

 of (vTj), which equation (7) connects with an energy - 

 transfer (TV/,?), the latter quantity will presently claim 

 attention. Next define ??j=w 1 2 2 = m / ' ; with v'~v, and 

 Q"=m"v. These lead at once to 



2v 1 T 1 -vT'-m 1 zh-~ = = z 1 [2v 1 T,-vT'-m 1 z*v'~], (9) 

 the factor (?,) being arbitrary. Finally it is evident that 



The supposition is continued, that C.G.s. units of length 

 and time (fluxion time) fix values for all observed velo- 

 cities ; either (v ) in the standard frame (F), or (v r ) in 

 any frame (U) . Therefore (dt —dtj) in the defining 

 ratios 



ClOC ^ i (XX ■ / "I 1 < 



dt ' dt ' 



the accents add only a helpful indication of the " observing- 

 frame. ; * This will not bar auxiliary time-differentials, lor 

 convenient expression of auxiliary velocities, originally 

 determined by c.G.s. units. Thus, if in relation to (F, U) 



, _ dt dx _ d /dx \ _ dv x _ di'i ) 



T ; dr ~ Vl ' Jr\aW) ~ clr ~ Z dto ; ! 



_dt ' d.Xo , , r d (dx f \ dvi _ jdvi 



j__dt d®o__j , __ / d fdx '\ 

 z dr dr \dr / 



dr' ~ ~ dt '' J 



Consequently, multiples of previous forces and activities 

 may be drawn upon for the algebra, from parallel series 

 like 



d 2 x „, dx / d 2 x \ d /m,V\ ^ ( ^ ^ 



m ^ = * T " ,77 h d?) = z JT { ■> I = -" S" = ,/t : ! (1;)) 



d?x ' , m , dn'o ( d 2 x '\ . d /wiv/ 2 v f dE' </E' I 



